A NOTE ON THE EQUIVALENCE OF THE PARITY OF CLASS NUMBERS AND THE SIGNATURE RANKS OF UNITS IN CYCLOTOMIC FIELDS. (27th June 2020)

• Record Type: Journal Article
• Authors: DUMMIT, DAVID S.
• Is Part Of: Nagoya mathematical journal. Volume 238(2020)
• Page Start: 206
• Page End: 214
• Publication Date: 2020-06-27
• Subjects: 11R18, -- 11R27, -- 11R29; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathematics; Wiskunde; Electronic journals; Periodicals; 510.5
• DOI: 10.1017/nmj.2018.42
• Languages: English
• ISSNs: 0027-7630

Abstract

Abstract : We collect some statements regarding equivalence of the parities of various class numbers and signature ranks of units in prime power cyclotomic fields. We correct some misstatements in the literature regarding these parities by providing an example of a prime cyclotomic field where the signature rank of the units and the signature rank of the circular units are not equal.